The slowly varying density approximation for the surface tension and surface energy of Lennard-Jones fluids revisited

We present a detailed study of the validity of the slowly varying density approximation to calculate the surface tension and the surface energy of Lennard-Jones fluids. To do so, we consider three explicit analytical expressions for the radial distribution function of the liquid phase, including one proposed by our research group, together with very accurate expressions for the liquid and vapour densities, also proposed by ourselves. The calculation of the surface tension from the direct correlation function using the Percus–Yevick and the hypernetted-chain approximations is also considered. Finally, our results are compared with those obtained by other authors by computer simulation, and also with those estimated via the general expressions (i.e., not in the ambit of the approximation studied here). We demonstrate that although the slowly varying density approximation is in good agreement with more complex expressions near the critical point, it is not adequate to calculate the surface energy and the surface tension of Lennard-Jones fluids at every temperature.